This is a slang that means something is coming from all directions. If things are coming in "left, right and center" they are definitely serious.

The expression comes from the military. In military terms on the battle field the commanders are concerned with getting "flanked" and have to be concerned with the strongest point of attack. When faced with an overwhelming attack which would see the opposition basically over running the defending unit the defending unit would simply refer to it as coming from "left, right and center" meaning everywhere.

In Britain any rich person will have insults coming left, right and center.